Equations of state based on lattice fluid have been providing alternative solutions to properties of real fluids. The abstract nature of lattice fluids has made it difficult to assess the connection between the model and real fluids. To elucidate the connection, the behavior of athermal lattice fluids was recently compared with molecular simulation data of hard-sphere chains. Athermal lattice fluids were found to provide an accurate representation of fused hard-sphere chains and a good approximation to contact hard-sphere chains when the segment number and hard-sphere volume are converted to their lattice counter parts. The behavior of associating lattice fluids were also compared and found to give approximations to those of associating hard-sphere chains with the same association energy when hard-sphere chain parameters are properly converted to lattice parameters. These findings lead to the lattice cell volume that is specific to species, based on which properties of pure species were found represented accurately with temperature independent parameters. Mixture formulation and some new applications were presented.